A Mathematical Model for Gas-Wiping Phenomena in Hot-Dip Galvanizing Process

Copyright !Cl IFAC Automation in the Steel Industry, Kyongju, Korea, 1997

A MATHEMATICAL MODEL FOR GAS-WIPING PHENOMENA IN HOT-DIP GALVANIZING PROCESS T.Kametani, K.Andachi, T.Nakagawa, H.Shigemoto, T. Yoshioka, M.Hirata J1iZLtshiJlla Works . Kall'Qsaki Steel COIporatioll . Kall'asakidori f -chome. MiZllshillla KLtrashiki 7 f 2. Japall pholle : 086-447-3609 E-mail : [email protected]. co.jp AbstractIn the gas wiping for continuous hot-dip galvanizing. a model analysis representing the relationship between its zinc coating weight and operating factors was carried out. By using this model taking the characteristics of two-dimensional free jet into consideration . new knowledge such as the fact that zinc coating weight is not influenced by its nozzle-slit gap in a jet range of narrow distance from nozzle to strip. etc .. were obtained. Also with this model verified in Mizushima CGL, it was confirmed that the calculated value of zinc coating weight was in good agreement with its measured values. Furthermore, with these knowledge applied to the improvement of its operation using a zinc coating weight control , an optimization of nozzle-sit gap. etc .. good results were achieved. Copyright © 1998 IFAC Keywords: distance. gap. gas, mathematical model , nozzles. pressure control , steel industry

operation .

1. INTRODUCTION Recently, a lot of high anticorrosion alloy hot-dip galvanized steel plates(GA) have been used as an exterior steel of automobiles . Therefore. the GA ratio accounting for the amount of production in the continuous hot-dip galvanizing line in our Mizushima Works is very high as well. Gas wiping is an important process in which the surface quality of this GA product is produced. Consequently, the relationship between its coating weight and operating factors, especially, the influence of nozzle-slit gap on its coating weight, and the relationship between the wiping nozzle and the strip in the range of a near distance are important for improving the wiping operations such as coating weight control. highspeed thin galvanizing. etc ..

2.MA THEMA TICAL MODEL FOR GAS WIPING In the gas wiping process. continuously annealed steel sheets are lifted up after the immersion in the molten zinc pot as shown in Figure 1, and its molten zinc liquid film adhered to the front- and back surfaces of the steel sheet is adjusted by a high pressure gas jet from its wiping nozzles arranged in the height of about 300-500 mm over the pot to a specified zinc coat weight (30-70glm2=4.5-9.0,u m). With Navier-Stokes equation applied with the boundary layer theory to the zinc liquid film adhered to the steel sheet lifted up from the zinc pot and the mass conservation method simultaneously arranged[ 11, and with the two dimensional jet theory[2] and isoentropic flow in the near field region and the far field region applied to the wiping jet, the relationship between the coating weight and the operating factor is

This paper reports that, with the model analysis of wiping phenomena carried out. this was verified in Mizushima CGL, and together with this, a good result was achieved by appl ying the above result to the coating weight control and the improvement of

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detennined. It is suggested that zinc coating weight is related to influencing factors as shown in equations (I) and (2) and the dependency on the distance from the nozzle to the strip varies in the near field region and the far field region by the characteristics of two dimensional jet flow jetting from a slit with a large aspect ratio, and the coating weight is not influenced by the nozzle-slit gap in the near field region. Also because of an influence of zinc temperature at wiping point. the above equations are constructed taking the change in wiping gas temperature in adiabatic expansion. zinc bath temperature, and heat transfer coefficient of wiping gas into consideration.

Wiping NozzIle H

Y

D

Tzo

~

\ TZn

zinc pot Fig . l-l Schematic of hot dip galvanizing process

I)

Near Field Region ( DIB K

W=k I X P X

(

2X

r;

~ C)

-I

X

Distance from nozzle to strip

) 0.5

K

X Pa

0.5 XD

Wiping Nozzle

I

u. X Y

X

(plP~)4_1

(

----- (I)

( , , ___
W=k2X

0

•

X

(

2X

r;

-I

X

)0.5 K

X Pa

X ( _ _~I.::...~_X_Y _ _ )0.5 ,,·1

...-.-J

,'"om ,;"ore

/""

~ Nozzle slit gap

8

f\-Y-~

2) Far Field Region ( D/B > C ) K

x_~

D

X--

B

ir~

0.5

Two dimensional jet

splash

----- (2)

(P/Pa)-"- _I

p

p

t)

B ; nozzle slit gap, D; nozzle-strip distance, H ; height of nozzle, P; nozzle plenum pressure, Pa; atomospheric pressure, Y ; strip speed , W; coating weight. r; ; nozzle efficiency, K ; ratio of specific heat of gas, p. ; molten metal viscosity, p ; molten metal density

Strip speed V Fig.I-2 Schematic of gas wiping process As shown in Figure 2, it is known that the wiping gas jet can be distinguished between the near field region containing a potential core on the central axis of the nozzle of which maximum gas flow rate is not damped and the far field region in which the maximum gas flow rate is damped with the increase of distance from nozzle. and they are represented by a different gas

3.VERIFICATION RESULTS OF MATHEMA TICAL MODEL

x

The analytical model was verified using experimental and operating data coIlected in Mizushima CGL. Zinc coating weight was evaluated using the measured value obtained from an on line coat weighting instrument and the value obtained from wet chemical analysis, and with the distance from the nozzle to the strip measured with a range finder installed immediately over the wiping nozzle. front and back surfaces of the strip were evaluated for each.

Vma~

I~

al~ Near field region

----

Far field region

Fig.2 Schematic representation of two dimensional subsonic turbulent free jet

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flow rate distribution for each. However, its boundary is different from its nozzle shapes, etc. In the nozzle of Mizushima CGL, its boundary is about DIE = 8 - 10 as shown in Figure 3.

The zinc coating weight is proportional to one second power of the distance from nozzle to strip in the near field region, and proportional to first power of that in the far field region. Consequently, it revealed that there is a different dependency on the distance from the nozzle to the strip.

Figure 4 shows the relationship between zinc coating weight and nozzle pressure. The zinc coating weight is proportional to one second power of nozzle pressure tenn and in good agreement with its model equation.

Figure 7 shows the comparison of the measured value of zinc coating weight obtained from the operating data in the near field region carried out varying the nozzle-slit gap with the calculated value from the model equation. In the near field region , it was confirmed that the zinc coating weight is not influenced by the nozzle-slit gap. Also the analytical model equation is capable of predicting the zinc

Also as shown in Figure 5, the zinc coating weight is proportional to one second power of strip speed. Figure 6 shows the relationship between zinc coating weight and distance from nozzle to strip.

I

,

I

I

I

I

key P-Pa [kPaj

200 N

E ~

~ .~

100 r-

vm'!=v~~_ VmlX =Y 0

50 r-

x ( D I B).{).5

r-

slope = I / 2

30.4

"V

60.8

0

75.0

/

-

_

,/

0

~~ ..o/"

~

./

c::

-

8

g 20 B = Base mm D=6mm

N 10~--~~~~~~~'----~~~

1

I

10

5 10 20 30 40 Strip Speed [m I sec] Fig.3 Damping characteristic of maximum wiping gas flow rate

2

I

I

200 100 Strip speed [ m/min ] Fig.5 Relation between zinc coating weight and strip speed 50

w.------------------------. key V [m/min] ;:- 100 E

0

120

6

90

~

80 r-

Woe D

N

E

))"

--. 70 re.a

!::()

00 .r:) 50 ~

'----

'----~

.§ u c

~

~~

!::()

6u

fo 601- Woe DO.5

. ;:)

slope=-1/2

e.o t:

~

0

u u

N B = Base mm D=6mm

10

I

I

I

40

r-

I-tI 0

00

t:

20 -

N

~o~ro

50 -

c;:

0

30

I-

20 4

/

V = 85-90 mlmin P-Pa= 44-49 kPa B = Base mm Gas temp. =30 "C

8 12 16 Nozzle-strip distance [ mm 1 Fig.6 Relation between zinc coating weight and nozzle-strip distance

I

0.05

0.10 0.20 0.50 r; . {(P/Pa)0288-1} [-] Fig.4 Relation between zinc coating weight and nozzle plenum pressure

61

20

70

r-------------------------~

key

60 N

E

~

N

B[mm)

•

Base - 0.65

0

Base - 0-10

t::.

Base

::

~50 01)-

.="fD

l~::

Target coating weight : Front 1 Back 41.1/41.4 ~27 .0/27.0

·····'-l

..

__. __

~-~-._-r~-_~ .~~~~~

50

30

20

Near field region V = 60 -120 mlmin P-Pa= 19.7 - 88.9kPa 20

30

60

~:J

50 Measured values [g/m 2 ) Fig.7 Comparison of calculated and measured coallng weight on near field region

8 ----------- \

~ ::

70

~

-

7f.-;

1'__----1.-----'-----...L..-----L--__--J

40

- - - Front surface of strip - - B;}ck surface of strip

~~ 12

' \:

~._~

~~

~----------~-----4

5min

~------~------

__~______-J

Time [min ) Fig.8 Autom;}ticall y coating weight controlled results

coating weight in the actual operation of Mizushima these concepts, with the nozzle-slit gap optimized, and together with the automation of zinc coating weight control and the improvement of control accuracy promoted, effects have been achieved for improving the operation .

CGL with the accuracy of ± 2g/m 2.

4.EXAMPLES OF RESULTS APPLIED TO ACTUAL MACHINES The automation of zinc coating weight control was achieved by introducing this analytical model to the automatic control of zinc coating weight in Mizushima CGL, and together with this, by improving its control system, and by introducing a range finder measuring the distance from nozzle to strip. Figure 8 shows an example of automaticaIly controIled results in the case that a targeted coating weight is same in front and back surfaces of strip (equal thickness galvanizing). At the point where a targeted coating weight is changed, its response is raised taking into consideration the lower limit of distance between nozzle and strip and the lowerand upper limits of nozzle pressure, and changing the distance from nozzle to strip and its nozzle pressure. Also in the case that a targeted coating weight is different in the front and back surfaces of strip(different thickness galvanizing),automatic controls are carried out independently for each of surfaces.

5.CONCLUSION The modcl which predicts the coating weight for gas wiping in hot-dip galvanizing process was devised and was applied in Mizushima CGL.

REFERENCES [1] I.A.Thomton and H.F.Graff (1976 ) : Met.Trans.,B,7b, , 106 [2JN.Rajaratnam (198\) ; " Turbulent Jets .. japanese translation Morikita pub . [3JK.Andachi, et al . (1993): ISD Meeting Materials and Processes,voI.6,No.5,430

It is considered that, based on this analytical model, zinc coating weight is not affected by the nozzle-slit gap in the near field region, and a thin galvanizing can be effectively achieved by narrowing the nozzle-slit gap, and suppressing its zinc splash and the lowering of zinc coating temperature. Based on

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